Interacting laminar shell structural component



c. PAYNE 3,349,525

URAL COMPONENT Oct. 31, 1967 2 Sheets-Sheet 1 Filed Jan. 14, 1966INVENTOR. CHARLES PAYNE Oct. 31, 1967 c. PAYNE 3,349,525

INTERACTING LAMINAR SHELL STRUCTURAL COMPONENT Filed Jan. 14, 1966 2Sheets-Sheet 2 INVEN TOR. CHARLES PAYNE m oiliamqg/ United States Patent3,349,525 INTERACTING LAMINAR SHELL STRUCTURAL COMPONENT Charles Payne,North Miami, Fla., assignor to Koppers ompany, Inc., a corporation ofDelaware Filed Jan. 14, 1966, Ser. No. 520,699 7 Claims. (CI. 52-80)This invention relates to structural members and more particularly to aninteracting laminar shell type of structural component in the form of apanel.

The structural advantage of a curved thin plate or laminar membrane hasnot heretofore been completely and fully developed in the building artsfor the reason that such curved membranes tend to buckle at relativelylow compressive loads and thus lose their structural effectivenessbefore they can be of any significant use. The problem becomes moreacute, as the compressive loads on the curved membranes increases. Inthe case of a double-curved membrane structure, particularly, it has notbeen possible to realize the full advantage of this type of membranebecause of premature buckling due to elastic instability at thethreshhold of the elasto-plastic range where the elastic modulus fallsoff. Heretofore, there has been no simple, satisfactory way toeffectively utilize the potential full structural capacity of a thinlaminar member.

The present invention, however, discloses a solution to the problem andincludes a laminar structural component in the form of a panel having aprimary or principal membrane, a secondary or back-up membrane which isthinner than the primary membrane, and an intermediary core which isbonded to both the primary and the secondary membranes. The primarymembrane is a portion of a synclastic surface, but it may also be aportion of an anticlastic surface, and the secondary membrane isgenerally an anticlastic surface.

For a further understanding of the present invention and for furtheradvantages and features thereof, reference may be made to the followingdescription taken in conjunction with the accompanying drawing whichshows, for the purpose of exemplification, a preferred embodiment of theinvention.

In the drawing:

FIG. 1 is a schematic perspective view looking downward at the top of aninteracting laminar shell structural component partly in section, inaccordance with the invention;

FIG. 2 is a schematic perspective view looking upward at the bottom ofthe laminar shell component of FIG. 1;

FIG. 3 is a schematic perspective view of a modification of theembodiment of FIG. 1;

FIG. 4 is a schematic perspective of a typical structure incorporatingthe laminar structural component of FIG. 1;

FIG. 5 is a schematic perspective view of the top laminar shell inanother embodiment of the invention;

FIG. 6 is a schematic perspective view of hyperbolic paraboloidalsurfaces subjected to a superimposed loading showing the forces actingbetween interacting hyperbolic paraboloidal surfaces; and

FIG. 7 is a schematic view of the such surface.

As used herein, a laminar membrane may be considered as a thin platehaving a small thickness in relation to its other dimensions. As usedhereinafter, a synelastic surface curves away from, in all directions, aplane tangent to the surface at a point of tangency. A typicalsynclastic surface is a spherical surface. An anticlastic surface curvesin one direction convexly along a longitudinal planar section andconcavely in another direction along a transversely planar sectionsubstantially perpendicular to the longitudinal plane. A typicalanticlastic forces acting in one surface is the surface of the saddle.

The interacting laminar shell structure 11 of FIG. 1 includes a top orsynclastic primary membrane 13, a secondary or anticlastic back-upmembrane 15 spaced apart from the primary membrane 13, and a core 17which is bonded to both the primary and the second membranes. Theperipheral edges of both the primary and the secondary membranes 13, 15may be, as illustrated herein, connected together by means of plate-likeweb members 19, which are generally trapezoidal in shape, as may benoticed from FIGS. 1 and 2.

In any particular application, such as for example, the portion of anantenna reflector 21 shown in FIG. 4, the reflector surface is made upof a plurality of edge abutting panels or prisms each of which wouldhave the form of the interacting laminar shell structure 11.

The primary membrane 13 may be either a single plate, as shown in FIGS.1 and 2, or it may be a structural sandwich type panel comprised ofadhesively secured layers, or a composite panel that is itself comprisedof inner and outer membranes fixedly connected to a preferred type ofcore reinforcement between the inner and outer membranes. It should beunderstood that the several interacting laminar shell structures 11comprising the structure shown in FIG. 4 may be fastened together in anysuitable mariner such as by welding-4f a weldable metal is used-or bybolts, or other type of fastener means well known in the art.

In a typical interacting laminar shell structure 11, the primarymembrane 13 may be a segment of the surface of: a paraboloid, a sphere,an ellipsoid, a cylinder, or any other like surface of revolution,whereas the secondary membrane 15 may be generally an anticlasticsurface, such as a segment of a hyperbolic paraboloidal surface. Asmentioned previously, the primary membrane 13 may be also anticlastic ifpreferred or desired.

In any particular interacting laminar shell structure, the secondarymembrane 15 is considerably less stiff than the primary membrane 13, andis generally thinner than the primary membrane. Therefore, the secondarymembrane acts as an elastic foundation for the primary membrane.Furthermore, the secondary membrane acts to support only the bucklingforces that develop in the primary membrane, and in so doing, thesecondary membrane stabilizes the primary membrane so that the primarymembrane can accept loads and stresses which approach, and in some casesexceed, the yield strength of the material of the primary membrane. Forexample, whenever the material of the primary membrane is a ductilematerial, the stress in the ductile primary membrane may be in theplastoelastic range, where stresses will exceed the yield strength ofthe material.

It is a feature of the present invention that the primary membrane 13 isstabilized by the secondary membrane acting through some form of coremedium 17. Buckling forces which develop in the primary membrane becauseof dimensional instability, or for any other reason, are transmitted tothe secondary membrane through the core system. The core system may be aseries of interconnected webs disposed in a cellular arrangement asshown in FIG. 1, or a honeycomb arrangement, or a solid core 23 of thetype suggested in FIG. 3. A typical solid core synthetic product whichis suitable for the purpose described herein includes a low-densityconcrete binder phase of hydraulic cement, a surface active additive,and an aggregative phase of expanded polystyrene particles, which ismarketed under the trademark Dycon. In any event, whatever type of coremedium is utilized, it must be bonded to both the primary membrane andthe secondary membrane for effective ness.

It, is also a feature of the present invention that the seat portion ofthe riding secondary membrane when loaded transversely by bucklingforces transmitted thereinto, acts to direct such forces along the edgesof the secondary membrane end through the points of connection into themain structural support, such as the support shown in FIG. 5, for theinteracting laminar shell structures.

It should then be evident to those skilled in the art, that the novelstructural panel component of the invention possesses numerous featuresand advantages not heretofore available in the art. That such astructural panel is adaptable to various types of buildings is evident,and to those structures the present invention contributes a significantreduction in weight, economy of construction, and a more efficientutilization of materials in the panels.

FIG. 5 illustrates another embodiment of a synclastic primary membrane23 in accordance with the invention wherein edge bands 25 are employedaround the periphery of the laminar membrane. Such edge bands 25 may, ofcourse, be employed around the periphery of all prism panels or laminarshell structures 11 and the edge bands 25, when used on the laminarshell structures 11 forming the typical structure 21 of FIG. 4, becomeinterlocked at the joints between four adjacent panels and substantiallystrengthen the entire structure 21.

The action of the edge band system may be multitudinous and redundantwhile the principal shell operates in the elastic range, dependingprimarily upon the conditions of support provided to the completestructure. However, the action of the structure may be readilyenvisioned. It must be remembered that as the primary membrane 13(FIG. 1) is permitted to flow, it generates lateral buckling forceswhich become transferred to the undulating back-up system through thecentral core. The back-up system or secondary membrane is considered tobe still operating in the elastic range.

For the type of structure 2.1 shown in FIG. 4, where the interactingback-up or secondary membranes 15 are hyperbolic paraboloids, transverseloading generates edge forces in the prism panels 11 which may besummarized (a) Internal thrusts generated along the paraboloidalelements;

(b) Compression forces in the convex parabolas; and

(c) Tension forces in the concave parabolas.

The equal thrusts exist on coordinates at to the linear edges, combiningas components of the characteristic system of internal edge forces.

The common characteristics of structural behavior for any arrangement ofinteracting laminar shell construction ground support equipment can besummarized as:

(1) A principal shell of double-continuous curvature, usually synclasicarranged to enclose a preselected space or to cover a preselected area.Except for considerations of dimensional stability, and in someinstances except for considerations of stable manner of shell actionsupport, the shell would generally be of conventional form to supportthe imposed loading conditions. In an interacting laminar shellstructure the primary membrane 13 carries the principal forces, orprincipal stresses, to internally resist and thus sustain the imposedloading;

(2) The primary shell or membrane 13, stabilized by the back-up orsecondary membrane 15 acting through some form of web or core such asthe cellular web system 17 in FIG. 1 or the solid web system 23 shown inFIG. 3. Transverse buckling forces which may be generated in the primarymembrane 13 because of dimensional instability, or for other reasons,are imposed upon the web system 17 or 23 and thus carried to the back-upor secondary membrane 15. Stating this another way, the primary membrane13 is continuously supported by the web system 17 or 23 against bucklingfrom inelastic effects or otherwise;

(3) The backup or secondary membrane 15 has imposed upon it, because ofits relative stiffness, essentially only the buckling forces which aregenerated in the primary membrane 13. And so, the primary membranemaintains its configuration and continues to carry the principal forcesup to the point of its ultimate strength;

(4) The pressure pattern of buckling forces in the primary membrane 13is directly imposed through the web system 17 or 23 upon each back-up orsecondary membrane and in the embodiments of the invention illustratedin the drawings, each back-up membrane is a hyperbolic paraboloidalsurface;

(5) The back-up membrane 15, loaded transversely by the buckling forcesof the primary membrane 13, acts in the manner characteristic of alldoubly-curved stiff membranes, to convert these transverse bucklingpressure forces to direct linear forces LF acting along the edges ofeach back-up membrane, the linear forces LF being shown schematically inFIG. 6. Thus, these linear forces LF are carried by the edge bands 23(FIG. 5) of each back-up membrane 15; and

(6) Generally there are edge bands 25 on the primary membrane 13directly opposed to edge bands 27 on the secondary membrane 15 (see FIG.7). Since the two sets of edge bands 25, 27 are connected by the coresystem 17 or 23, a structural system is formed which also has acurvilinear conforming rectilinear grid pattern. The direct forcesacting along the edge bands of each back-up membrane 15 are thus throwninto this edge band structural system as coplanar forces. Consequently,the transverse pressure pattern of buckling forces, transversed from theprimary membrane to the secondary membrane through the web or coresystem, is converted to linear forces which are coplanar with the edgeband system. Such coplanar linear forces LF are suggested in FIG. 6.

It should be clear that provided the primary membrane is not stable asan entity, then its lateral buckling force pressures are supported, atall places upon the surface, by a back-up shell system which convertsthese pressure forces to linear forces in a three-dimensional networkand effectively distributes these to a well balanced condition.

Although the invention has been described herein with a certain degreeof particularity, it is understood that the present disclosure has beenmade only as an example and that various modifications and changes maybe made Within the scope of the invention as defined by the appendedclaims.

What is claimed is:

1. A structural component comprising:

(a) a primary membrane having the shape of a portion of a surface ofrevolution;

(b) a secondary membrane spaced apart from said primary membrane andhaving the shape of a hyperbolic paraboloid; and

(c) a core system bonded to both said primary and said secondarymembranes whereby buckling stresses which develop in said primarymembrane when a load is applied to said panel are transmitted to saidsecondary membrane.

2. A structural component comprising:

(a) a primary membrane having a synclastic form;

(b) a secondary membrane spaced apart from said primary membrane andhaving an anticlastic form, said secondary membrane being thinner thansaid primary membrane; and

(c) a solid core bonded to both said primary and said secondarymembranes, whereby said primary membrane and said secondary membranecooperate to significantly reduce buckling in said primary membrane whenthe same is under stress.

3. A structural panel comprising:

(a) a primary membrane having the form of a portion of a sphere;

(b) a secondary membrane having the form of a hyperbolic paraboloid,said secondary membrane being thinner than said primary membrane andspaced apart therefrom;

(c) a web member fixed adjacent the peripheral edges of both saidprimary and said secondary membranes; and

(d) a core bonded to both said primary and said secondary membraneswhereby buckling stresses developing in said primary membrane when aload is applied to said panel are transmitted through said core to saidsecondary membrane.

4. A structural panel comprising:

(a) a primary membrane having an antiol-astic form;

(b) a secondary membrane spaced apart from said primary membrane andhaving an anticlastic form, said secondary membrane being thinner thansaid primary membrane; and

(c) a core bonded to both said primary and said secondary membraneswhereby said primary membrane and said secondary membrane cooperate tosignificantly reduce buckling stresses developing in said primarymembrane when a load is applied to said panel.

5. The invention set forth in claim 3 wherein:

(a) said core is comprised of a synthetic solid product, including alow-density concrete binder phase of hydraulic cement, a surface-activeadditive, and an aggregative phase of expanded polystyrene particles,that is bonded to substantially all of the opposed surfaces of saidprimary and said secondary membranes.

6. The invention set forth in claim 3 wherein:

(a) said core is comprised of intersecting mutually cooperative Webmembers bonded to a portion of each of the opposed surfaces of saidprimary and secondary membranes.

7. The invention set forth in claim 3 wherein said secondary member isan elastic foundation for said primary member.

References Cited UNITED STATES PATENTS 2,912,840 11/ 1959 Baroni 52803,292,315 12/1966 Silberkuhl et al 52-80 3,296,754 1/ 196-7 Silberku'hlet al. 5280 20 FRANK L. ABBOTT, Primary Examiner.

C. (j. MUELLER, Examiner,

1. A STRUCTURAL COMPONENT COMPRISING: (A) A PRIMARY MEMBRANE HAVING THESHAPE OF A PORTION OF A SURFACE OF REVOLUTION; (B) A SECONDARY MEMBRANESPACED APART FROM SAID PRIMARY MEMBRANE AND HAVING THE SHAPE OF AHYPERBOLIC PARABOLOID; AND (C) A CORE SYSTEM BONDED TO BOTH SAID PRIMARYAND SAID SECONDARY MEMBRANES WHEREBY BUCKLING STRESSES WHICH DEVELOP INSAID PRIMARY MEMBRANE WHEN A LOAD IS APPLIED TO SAID PANEL ARETRANSMITTED TO SAID SECONDARY MEMBRANE.